sympathize vs pity

sympathize is not a noun while pity is a noun.

Word	Noun	Adjective	Verb	Adverb
sympathize	No	No	Yes	No
pity	Yes	No	Yes	No

As verbs, pity is a hypernym of sympathize; that is, pity is a word with a broader meaning than sympathize:

Other hypernyms of sympathize include compassionate, condole with, feel for, sympathize with.

sympathize (noun)	pity (noun)
	the humane quality of understanding the suffering of others and wanting to do something about it
	an unfortunate development
	a feeling of sympathy and sorrow for the misfortunes of others

sympathize (verb)	pity (verb)
be understanding of	share the suffering of
to feel or express sympathy or compassion
share the feelings of; understand the sentiments of